Method and apparatus for grinding and polishing aspheric surfaces of revolution



D. VOLK Oct. 27, 1970 METHOD AND APPARATUS FOR GHINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION 9 Sheets-Sheet l Filed Oct. 16. 1967 Ummlwm TD/PNEYS D. VOLK Oct. 27, 1970 METHOD AND APPARATUS FOR GRINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION 9 Sheets-Sheet 2 Filed OCT.. 16. 1967 D. voLK 3,535,825 METHOD AND APPARATUS FOR GRINDING AND POLISHING Oct. 27, 1970 ASPHERIC SURFACES OF REVOLUTION 9 Sheets-Sheet 5 Filed Oct. 16. 196'? Oct. 27, 1970 D. VOLK 3,535,825

METHOD lAND APPARATUS FOR GRINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION Filed Oct. 16. 1967 9 Sheets-Sheet 4 F( ,0 F H /7 f 0 ,F f7

Oct. 27, 1970 D. VOLK 3,535,825

METHOD AND APPARATUS FOR GRINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION Filed Oct. 16. 1967 9 Sheets-Sheet 5 Oct. 27, 1970 D. VOLK 3,535,825

METHOD AND APPARATUS FOR GRINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION Filed Oct. 16. 1967 9 Sheets-Sheet 6 INVENTOR. DIV/0 VOL K D. voLK 3,535,825 METHOD AND APPARATUS FOR GRINDING AND POLISHING Oct. 27, 1970 ASFHERIC SURFACES OF REVOLUTION 9 Sheets-Sheet 7 Filed 001'.. 16. i967 Oct. 27, 1970 D. voLK 3,535,825

METHOD AND APPARATUS FOR GRINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION 9 Sheets-Sheet 8 Filed Oct. 16. 1967 IM'ENTOR. .DAW/.0 Vom BY @MM5 QL/ Oct. 21, 1970 D. voLK 3,535,325

METHOD AND APPARATUS FOR GRINDING AND POLISHING ASPHERIC SURFACES OF REVOLUTION Flled Oct 16 1967 9 Sheets-Sheet u I EQ 1N vENToR. /yl//D VOL A* United States Patent Otice Patented Oct. 27, 1970 U.S. Cl. 51-124 8 Claims ABSTRACT OF THE DISCLOSURE A method and apparatus for forming aspheric surfaces of revolution for lenses and the like utilizes two contacting surfaces of revolution, each rotating about an axis of revolution with one of these surfaces being generally convex and the other being generally concave. If the tool is the convex surface then a negative surface of revolution will be formed on the lens, whereas if the tool is the concave surface, then a positive surface of revolution is formed on the lens. The useful area of the generally convex surface is generally toric, and lies in a zone between two circles of latitude with almost any point in the zone having a transmeridional radius of curvature greater than its meridional radius of curvature and the trensmeridional radii of curvature increase continuously and regularly from the largest circle of latitude to the smallest circle of latitude in that zone. The generally concave surface of revolution is of generally conicoid shape in the contacting area of which the meridional radius of curvature increases continuously and regularly from the apex to the periphery of the surface. The axes of revolution of the convex and concave surfaces intersect at all times and relative oscillation between the surfaces occurs in a generally meridional direction of the convex surface with the axis of revolution of the concave surface being approximately normal at all times to the convex surface.

This invention relates to a method and apparatus for generating, grinding and polishing surfaces of revolution on optical material of glass, plastic, or metal, in particular concave aspheric surfaces of revolution having an apical umbilical point, including prolate ellipsoids, paraboloids and hyperboloids, and as the limiting case of the prolate ellipsoid, the sphere, and surfaces closely resembling said conicoids, described in my patents, Lens Generating Method, No. 3,218,765, granted Nov. 23, 1965, and Lens Surface Generator, No. 3,239,967 granted Mar. l5, 1966, and including bell shaped surfaces of revolution with an apical umbilical point in which a meridian section of said surface has a point of inflection, with the surface having negative curvatures central to the. circle of points of inflection, and having positive curvatures meridionally and negative curvatures transmeridionally peripheral to said circle of points of inflection.

The method and apparatus of this invention can also be used to generate, grind and polish negative surfaces of revolution having a distinct central area which is either spheric or aspheric, said area adjoining but optically distinct from a peripheral zone which may be either spheric or aspheric.

The method and apparatus of this invention is useful for the production of glass and metal aspheric surfaces of revolution which serve as molds or forms for the molding and casting of plastic lenses as well as for the generating, grinding and polishing of lens surfaces directly on optical material.

The method and apparatus of this invention may also be used for the generating, grinding and polishing of surfaces of revolution of positive curvature which are of generally toric shape, and the description of this aspect of the invention will follow that for the generating, grinding and polishing of surfaces of revolution which are generally concave.

The method and apparatus of this invention is particularly applicable to the polishing of the concave conicoids 0f revolution serving as the corneal surface of aspheric contact lenses described in my copending patent application, Aspheric Corneal Contact Lens Series, Ser. No. 492,408, `tiled Oct. 5, 1965, said conicoids generated by methods and apparatus described in my Pat. No. 3,344,- 692, granted Oct. 3, 1967 for Method and Apparatus for Producing Aspheric Contact Lenses.

The shape of a conicoid of revolution, including the prolate ellipsoid, the paraboloid, and the hyperboloid, can be specified by its eccentricity, e, where e is the change in focal radius of a meridian section of the conicoid with respect to the vertex depth of the surface. Expressed as a differential equation:

ezdf/dx (l) where f is the focal radius of the conic section, and x is the coordinate along the axis of revolution of the conicoid, with the apex of the conicoid as the origin. The conicoids of revolution are a special class of surfaces whose shapes are uniquely expressed by their eccentricites, where the eccentricity is constant for any given conicoid.

Characteristic of the above named conicoids is the fact that the meridional and transmeridional curvatures decrease continuously and regularly from the apex outward, as a function of the apical radius of curvature and eccentricity of each conicoid (this being true for the prolate ellipsoid up to the point of intersection of the meridional Curve and the minor axis of the elliptical meridian section).

There are a great many other surfaces of revolution with apical umbilical points which resemble the conicoids of revolution and, for an area about their apices, one is substantially correct in specifying the shape of these surfaces in terms of eccentricity. However, when the full extent of such a surface is taken into account, its shape cannot be specified by a single number, i.e., eccentricity. These non-conicoid surfaces of revolution can be matched or osculated at their apices by conicoids, a specific nonconicoid surface being osculated by a specific conicoid which is defined by its apical radius of curvature and its eccentricity. Beyond the area of osculation and out to its peripheral limit, the rate of decrease in meridional curvature of the non-conicoid surface may accelerate with respect to that of the osculating conicoid, so that said conicoid lies within said non-conicoid, or the rate of decrease in meridional curvature of said non-conicoid surface may decelerate with respect to that of the osculating conicoid, so that although said nonconicoid surface is one of decreasing meridional curvature peripheralward, the osculating conicoid will lie outside of said surface.

In the drawings,

FIG. 1 is a diagram showing modified conicoid arcs osculated by a conicoid and by a circle;

FIGS. 2A, 2B and 2C are sections through bell shaped surfaces;

FIG. 3 is a plan view of the generally convex toric surface of this invention;

FIG. 4 is a diagrammatic view of FIG. 3 explaining the principles of this invention;

FIG. 5 is a diagrammatic view showing the contacting generally convex and generally concave surfaces of this invention;

FIGS. 6a through 6j illustrate the changing areas of abrading contact on the work piece as relative oscillation occurs between a concave work piece and a convex tool;

FIG. 7 is a side elevational view of the convex tool in FIG. showing the sequence of abrading areas as the work piece is oscillated;

FIG. 8 is a top plan view of the tool in FIG. 5 showing the same sequence of abrading areas during oscillation of the work;

FIG. 9 is a central sectional view through a lens work piece and its holder showing how it may be supported while in contact with the tool;

FIGS. 10 and 1l are diagrammatic views similar to FIG. 4 explaining this invention when the semi-meridian section of the tool contains an elliptical arc, FIG. 10 showing the center of curvature of said elliptical arc at the equatorial plane of symmetry on the tool below the axis of revolution of the tool; and FIG. 11 showing the same center above the axis;

FIGS. 12, 13 and 14 are diagrammatic views similar to FIG. 4 explaining this invention when the semi-meridian section of the tool is a cycloid, and respectively showing the center of curvature of said cycloidal arc at the equatorial plane of symmetry of the tool on, below and above the axis of revolution of the tool;

FIGS. 15, 16 and 17 are diagrammatic views similar to FIG. 4 explaining this invention when the semi-meridian section of the tool is the involute of a circle, and respectively showing the center of curvature of said involute at the equatorial plane of symmetry of the tool on, below and above the axis of revolution of the tool;

FIGS. 18, 19 and 20 are diagrammatic views similar to FIGS. 15, 16 and 17 respectively, only having a smaller circular evolute CF and CF';

FIG. 211 is a diagrammatic view showing a limiting case of FIGS. 18, 19 and 20 in which the circular evolute is reduced to zero;

FIG. 22 is a meridian section of a tool resembling FIG. 21 but with the semi-meridian section being an elliptical arc;

FIG. 23 is a meridian section similar to FIG. 22 except that the axis of revolution of the tool intersects the major axis of the elliptical section at a distance greater than the semi-major axis;

FIG. 24 is a meridian section similar to FIG. 22 except that the axis of revolution of the tool intersects the major axis of the elliptical section at a distance less than the semi-major axis;

FIGS. 25 and 26 are perspective views of apparatus for carrying out the first embodiment of this invention, the two views being taken approximately 90 apart;

FIG. 27 is a fragmental view taken from the position of line 27-27 of FIG. 25;

FIG. 28 is an elevational view of the tool of the first embodiment of this invention showing a polishing cloth in section;

FIG. 29 shows elements to be substituted in FIG. 25 and FIG. 2-6 to carry out the second embodiment of this invention;

FIG. 30 is an enlarged view of the lower left-hand portion of FIG. 29;

FIG. 31 is a plan view of a work piece holder to be substituted in FIG. 29; while FIG. 32 is a top plan view of parts which may be substituted at the right-hand side of FIG. 26.

In FIG. 1, I have drawn the meridian sections of two non-conicoid surfaces Y and Z and their osculating conicoid X which lies within one of said meridian sections, Y, and outside of the other, Z, and have also drawn the osculating circle W whose radius of curvature is the apical radius of curvature of the said three meridian sections. The meridian sections of the non-conicoid surfaces depicted in FIG. l correspond to those of said other surfaces of revolution which resemble the conicoids of revolution, described above. To such non-conicoid surfaces which decrease continuously and regularly in meridional curvature from the apex peripheralward, though closely resembling their osculating conicoids, I have given the name modified conicoids.

The shape of meridian sections of said non-conicoid surfaces of revolution may be expressed in terms of eccentricity, but in a generalized form, such as in the form of a Taylor series, which takes into account the rate of change of eccentricity. Using MacLaurins formula:

3 3 2 4 6PM/a+ (demenza-kung? )x +---('if/fffmq m where eg can be defined as the generalized, or effective eccentricity. It is to be noted that when the derivatives of ee-edf/dx vanish, generalized eccentricity becomes simply eccentricity as defined in Eq. 1. so that eccentricity, in effect, is a special or limiting case of generalized eccentricity. Hence, by means of Eq. 2, the shape of the full extent of a meridian section of a modified conicoid may be expressed in terms of eccentricity and its derivatives. When the derivatives are a negative contribution to generalized eccentricity, the modified conicoid will lie within the osculating conicoid. Such generalized eccentricity I have termed hypoeccentricity, and the modified conicoid is said to be hypoeccentric. When the derivatives are a positive contribution to generalized eccentricity, the modi fied conicoid will lie outside of the osculating conicoid. Such generalized eccentricity I have termed hypereccentricity, and the modified conicoid is said to `be hypereccentric. When the derivatives of generalized eccentricity vanish, the surface is a conicoid, which by analogy with the above terminology, is an eccentric surface, whose shape is defined by its eccentricity. All hypoeccentric and hypereccentric modified conicoids osculated by a conicoid of specific eccentricity can be said to constitute a family of' isoeccentric surfaces, which also includes the eccentric surface whose eccentricity defines the family, and any given family of isoeccentric surfaces is further characterized by a magnitude factor, which is its apical radius of curvature. In a family of isoeccentric surfaces, the degree of hypoeccentricity or hypereccentricity of a modified conicoid may be stated in general terms as minimal, moderate, or severe, depending upon the rate at which the modified conicoid departs in curvature from the osculating conicoid.

Bell shaped surfaces of revolution may also be osculated at their apices by conicoids of revolution of given apical radii of curvature and eccentricities, but differ from modified conicoids in that meridian sections of said bell shaped surfaces have a point of inflection, .e., a reversal in curvature at said point. The shapes of meridian sections of said bell shaped surfaces may also be expressed, by means of Eq. 2, in terms of generalized eccentricity, FIGS. 2A, 2B and 2C are examples of bell shaped surfaces. Hereinafter such bell shaped surfaces of revolution will be treated as generally conicoid.

The initial process of generating an optical surface implies the relatively quick removal of relatively large amounts of the optical material, generally, though not necessarily, with tools containing abrasive diamond particles, to obtain the rough surface of desired contour, in contrast to grinding an optical surface, in which relatively small amounts of said material are removed to smooth the surface and perfect the contour, preparatory to polishing. Alternatively, the desired contours can be generated or roughed on optical material by grinding initially with large size abrasive particles until the desired surface contour is obtained, and this in turn is followed by grinding with much finer abrasive suspensions to obtain a very smooth surface ready for polishing. The use of diamond charged laps for grinding optical surfaces, rather than abrasive suspensions between the lap and the work material, makes it possible to both shape and smooth the optical surface in one operation, to the point where polishing can be commenced. In such cases, generating and grinding can be considered one and the same process. The combined process is especially worthwhile in the shaping of plastics, methyl methacrylate being one example of such plastics, in which the work material can be removed rapidly, and in the shaping of glass which is already close to the desired shape as a result of previous molding. With regard to polishing a smoothed optical surface, the process can be identical to the grinding process with the exception that the polishing tool or lap is made of, or covered with, a comparatively yielding substance such as pitch or felt cloth, and the abrasive is a suspension of extremely fine particles such as rouge, cerium oxide, or tin oxide` Thus the method and apparatus for generating, grinding and polishing according to this invention can be essentially similar.

In this invention, generating, grinding, and polishing all utilize the same method and apparatus. For generating and grinding, the tool of this invention may be made of cast iron or other metal, or plastic, or of a hard fibrous material, to be used with loose abrasive particles such as Carborundum or emery. Alternatively, the generating and grinding tools may be made of metal charged with diamond particles, said tools to be used with a liquid lubricant and coolant, so that loose abrasives or abrasive suspensions need not be applied to the tool during the generating and grinding procedures. I prefer to use the diamond charged tools since they may be used repeatedly for generating and grinding an extremely large number of optical surfaces without appreciable wear, whereas nondiamond charged tools wear rapidly. Hereinafter I will consider the generating and grinding tools to be of the diamond charged type although it is to be understood that the method and apparatus of this invention contemplates the use of both the diamond charged tool and the tool without diamond particles. For polishing, the tool is covered with an adherent soft cloth such as Velveteen, produced by Econ-O-Cloth, Chicago, Ill., and a suspension of said polishing abrasive, tin oxide for example, is constantly applied to the polishing tool during the polishing procedure.

When rapid generation of an optical surface is desired, the diamond particles in the generating tool are of relatively large size. The generated surface is then rough, covered with pits and scratches. Heretofore, the removal by grinding of said pits and scratches remaining after the generating of an aspheric concave optical surface of revolution has required either` (l) an exactly matching coaxial rigid grinding lap which is rotated against the lens surface with a thin layer of abrasive suspension between the two surfaces, a method which tends to produce concentric grooves in the optical surface as well as a defect at its apex, and (2) grinders which depend upon the resiliency or exibility of the grinding material used as the tool surface, including the supporting structures or materials, and (3) the use of multiple small metal facets as grinders, each facet being independently displaceable with respect to adjacent facets. In (2) and (3) above, though smoothing of the surface can be achieved, great care must be used so as not to deform the generated surface. Furthermore it is impossible to use (2) and (3) on small highly curved concave surfaces of contact lenses, without serious surface deformation.

In the method and apparatus of this invention, one tool can perform all of the process steps if used as herein described. Also, a single tool is capable of generating and grinding a large number of concave aspherical surfaces of revolution and others resembling bell shaped surfaces hereinbefore described, without producing concentric grooves in the surface or defects at the apex of the surface. Similarly, a single rigid tool, adapted for polishing by being covered with an adherent soft polishing cloth, is capable of polishing a large number of the above ground surfaces, without significant alteration in surface contour caused by the polishing process. Hereinafter, to avoid repetition, I will speak of the method and apparatus of this invention for grinding only, although it is to be understood that the description also applies to the method and apparatus of this invention for the generating and for the polishing of optical surfaces.

The grinding tool of the first embodiment of this invention is a cup shaped surface of revolution symmetrical about a plane perpendicular to its axis of revolution. Said plane shall hereinafter be termed the equatorial plane, and the circular section of said surface by said plane shall be termed the equatorial circle of latitude or equatorial circle or equator. A meridian section of said grinding tool may take one of several forms, but the essential feature of all tools of this invention is that the transmeridional radius of curvature increases continuously and regularly from a minimum value either at the equator of the tool or at a predetermined proximal circle of latitude near the equator of the tool, to a maximum value at a distal circle of latitude (farthest from the equator); the meridional radius of curvature may decrease continuously and regularly from a maximum value at the equator to a minimum value at a point farthest from the equatorial plane, or it may remain constant, or it may increase continuously and regularly from a minimum value at the equator to a maximum value at a point farthest from the equatorial plane. In any case, the transmeridional radius of curvature between said proximal and distal circles of latitude is greater than the meridional radius of curvature.

One form of the grinding tool of this embodiment of this invention which I have used successfully for the grinding and polishing of concave aspheric surfaces of revolution is shown in FIG. 3. FIG. 4 is a view perpendicular to a plane section of FIG. 3, i.e., a meridian section of the tool, said section containing the axis of revolution, X'X, of the tool. Since the tool is symmetrical about X'X, I will describe the geometry of only the arcuate portion of the upper half of FIG. 4, said arcuate portion hereinafter called a semi-meridian section of the tool, it being understood that all meridian sections of a surface of revolution are identical and symmetrical about the axis of revolution. Arc ABA is one half of an ellipse whose major axis is A'A and whose minor axis is B'B, the two axes which are parallel and perpendicular respectively to X'X, and intersecting at point O, the geometrical center of the ellipse whose semi-major axis OA is of length a, and whose semi-minor axis OB is of length Point C at one end of the evolute of elliptical arc ABA is at the perpendicular intersection of the minor axis BB of the ellipse and the axis of revolution X'X of the tool and is therefore at the center of the equatorial circle of latitude of the tool, points B and E being at opposite sides of the tool.

Arc CF is that branch of the evolute of the meridian section of the tool corresponding to elliptical arc segment BA, and by symmetry about the equatorial plane, arc CF is that branch of the evolute of the meridian section of the tool corresponding to elliptical arc segment BA'. Since the radius of curvature of any point on an elliptical arc is the distance along the normal from said point on the arc to the point of tangency of said normal to the evolute of said arc, radius of curvature r=CB of the elliptical are at the equator of the tool, i.e., the meridional radius of curvature of the tool, at that point, is exactly equal to the transmeridional or equatorial radius of curvature. Hence, the equatorial circle of the tool is an umbilical line. However, at all points along the elliptical meridian arc at increasing distances from the equator, the transmeridional radius of curvature of the tool is increasing while the meridional radius of curvature is decreasing. This is illustrated in FIG. 4 by a series of points, l, 2, 3 and 4 along the elliptical meridian arc. Consecutive normals from `said points are tangent to the evolute CF at continuously decreasing distances while said normals intersect the axis of revolution of the tool, X'X, at points l', 2', 3 and 4', continuously increasing in length, and it is precisely the distances 1-1, 2 2', 3 3' and 4-4' which are the transmeridional radii of curvature of the points l, 2, 3 and 4 on the tool.

The continuously increasing transmeridional radius of curvature of the tool from the equator or a nearby circle of latitude outwardly, is an essential quality of the tool of this invention. I shall hereinafter refer to this aspect of the tool design as transcrescence. Thus a tool with a low degree of transcrescence changes relatively slowly in its transmeridional radius of curvature along a meridian of the tool, from the equator or predetermined circle of latitude, while a somewhat similar tool which has a high degree of transcrescence changes relatively rapidly in its transmeridional radius of curvature along a meridian, from said equator or predetermined circle of latitude.

An example of a specic tool which I have used, said tool made according to the descriptions of FIGS. 3 and 4, is the following: r=CB, the radius of the equatorial circle, is 7.5 mm., which is also the meridional radius of curvature at the equator. The elliptical arc of the semimeridian section is that of an ellipse of eccentricity, e=.5. The length of the tool, A'A=2a, where a is the length of the semi-major axis of said ellipse, is 13 mm., while the length of the semi-minor axis of said ellipse, is 5.63 mm.

The relationship between a, r, and is given by the following equation:

azi-(l-ezf (3) The relationship between a, and r is:

By means of Equations 3 and 4, a wide range of tool shapes, of the form shown in FIGS. 3 and 4 may be designed.

In FIG. 5, I have drawn to scale the tool of the above example with a work piece, having as its ground surface a negative conicoid of revolution, applied to it in two different positions. Said negative surface, hereinafter called a work surface, has an apical radius of curvature of 7.5 mm. and an eccentricity of .7, and a diameter of 11 mm., and it can be generated by the method and apparatus described in my Pat. No. 3,344,692, granted Oct. 3, 1967 for Method and Apparatus for Producing Aspheric Contact Lenses. The work piece or button can be made of methyl methacrylate, and is approxi mately 3 mm. thick at its center, the extra thickness of material to be later removed in finishing the front surface of the lens. The button, held by means of a work holder to be later described, is applied to the upper aspect of the tool, the axis of the work surface lying in the equatorial plane, so that the tool osculates the negative conicoid work surface at its apex. The work piece may be kept against the tool by means of gravity or by mechanical means. The tool is caused to rotate about its axis of revolution at approximately 1000 revolutions per minute, by means to be described later, and the work piece and its holder are likewise caused to rotate about their common axis of revolution at a somewhat slower rate, by means to be described later, varying from 60 to 300 revolutions per minute, while at the same time the rotating work piece and holder oscillate smoothly along the tool in a meridional direction (latitudinally) of the tool, at a rate of about 60 cycles per second, the range of oscillation, hereinafter called the stroke, extending from its initial position at or proximal to the equator to an end or distal position where the periphery of the work surface is being ground, as shown in FIG. 5. Only onehalf of the tool, i.e., on one side of the equator, need be used in the method of this invention for this embodiment. In the example, the stroke covers a distance of about 5 mm. along a meridian of the grinding surface of the tool, during which excursion the axis of revolution of the work surface will have changed its slope about 50 from its initial position.

In this method of grinding, the smoothing of said work surface is a continuous process in which the area of said work surface between its apex and periphery is being ground in continuously outwardly and inwardly moving zones consequent to the latitudinal sliding movements of the button on the tool, away from and towards the equator of the tool respectively. FIGS. 6a, b, c, d, e, and f, demonstrate on the work surface six consecutive positions of the outwardly moving zone of grinding contact resulting during a single stroke of the work piece. When the rotating work piece is over the equator of the rotating tool, the apical area of the work surface is being ground, FIG. 6a, and as the work surface moves smoothly along the tool away from the equator, the more highly curved apical area of the work surface is gradually lifted away from the tool, commencing with an arcuate area of grinding contact between the tool and the work surface which is attening, said arcuate area of contact being slightly convex upward, FIG. 6b. With further movement of the work piece latitudinally (FIGS. 6C and dl, the area of grinding contact between the work surface and the tool gradually divides into two symmetrical arcuate areas of grinding contact between the rotating tool and rotating work surface, which continues to flatten, lifting the work surface still further from the tool, said arcuate areas of grinding contact, FIG. 6d, being more highly curved upward as well as displaced upward on the work surface which is tilted. As a consequence of the transcrescence of the tool and the continuing latitudinal movement of the work surface, the central area of the rotating work surface which becomes free of contact with the surface of the rotating tool, is increased in size. With still further latitudinal movement of the work surface, FIGS. 6e and 6f, the two symmetrical arcuate areas of grinding contact between the rotating tool and the rotating work surface, shift continuously peripheralward on the work surface, where said arcuate areas of grinding Contact, though shorter in length, are even more highly curved upward, the entire work surface having been subjected in a continuous and regular manner to the grinding procedure or process, whereupon the direction of the stroke is reversed, with the sequence of areas of grinding contact also reversed.

In FIG. 7, I have drawn a lateral view of the tool of FIG. 5, showing the sequence of the areas of grinding contact on the surface of the tool, labeled a, b, c, d, e and f, which correspond to the sequence of areas of grinding contact on the work surface, as depicted in FIGS. 6a, b, c, d, e and f. It is to be understood that a view of the tool surface from the opposite direction would be like a mirror image of FIG. 7, since the areas of grinding contact on the tool surface are symmetrical about the vertical meridian plane, which corresponds to the plane of the drawing of FIG. 7, since the axis of revolution of the work surface lies in a vertical plane.

In FIG. 8, I have drawn a top view of the tool of FIG. 5, showing the same sequence of symmetrical areas of grinding contact, shown on one side of the plane of symmetry in FIG. 7. It is to be understood that these areas of grinding contact represent momentary stages during the grinding process which actually is continuous and smooth. Thus in the novel grinding method and apparatus of this embodiment of this invention, with each oscillation, the areas of grinding contact between the work surface and the tool move continuously and regularly from a single area of grinding contact centrally on the work surface, to a pair of symmetrically positioned peripheral f arcuate areas of grinding contact on the work surface,

and then back to a single central area of grinding contact, while on the surface of the tool associated areas of grinding Contact move, continuously and regularly, latitudinally on the tool.

For the grinding of continuous aspheric surfaces, the stroke must be smooth and continuous, Le., the work piece must not be allowed to dwell at any point during the stroke except momentarily at the ends of the stroke when the direction of the stroke is reversed. For the purposes of this invention, the oscillations of the work piece are, for the most part, essentially simple harmonic motion, differing from true harmonic motion in that the work piece must follow an arcuate path as it moves latitudinaly along the tool. It is to be understood, however, that the nature of the oscillations can be varied to suit special grinding needs. For example, I will later show that in Certain instances the work surface may be allowed to dwell in certain positions in order to produce surfaces divided into two or more different zones. Again, the oseillations, though regular and Continuous, may differ markedly from simple harmonic motion in order to subject certain areas of the work surface to unusual amounts of grinding action.

In the method and apparatus of this invention for grinding continuous aspherie surfaces, not only is the grinding a continuous process traversing the entire work surface, but the oscillatory motion has the effect of distributing wear over the surface of the tool. Furthermore, since both the tool and the work are rotating and, in addition, the work is oscillating, contacting points on the two surfaces are always at cross paths, so that at no time during the grinding procedure is there parallel motion between a point on the rotating tool and a contacting point on the work surface. Consequently, the apex of the work surface will not be deformed nor will concentric grooves or rings develop on the Work surface.

The length of the stroke necessary for the grinding of an entire work surface is a function of several interdependent variables related to both the tool and the work surface. The variables and their interrelations and effects can be listed and stated in general terms as follows:

(l) The magnitude of the work surface, i.e., its apical radius of curvature and its diameter. In general, the stroke is proportional to the magnitude of the surface. Small highly curved surfaces will require a small stroke compared to large, less highly curved surfaces.

(2) The diameter of the work surface. In general, the larger the diameter of a Specific surface, the larger is the stroke required, and vice versa.

(3) The eccentricity, or hypereccentricity, or hypoeceentricity of the work surface. In general, the greater the eccentricity, the longer the stroke required. If an eccentric surface ot` a given apical radius of curvature, eccentricity, and diameter, requires a specic length stroke, than a hypoeccentric surface of the same isoeccentric family and of the same diameter, will require a shorter stroke, while a hypereccentric surface of the same isoeccentric family will require a longer stroke.

(4) Bell shaped surfaces. In general, bell shaped surfaces require a longer stroke than conicoids and modified conicoids of similar magnitude and diameter.

(5) The transcrescence of the tool. For a given conicoid, modified conicoid, or bell shaped surface, of a given diameter and given apical radius of curvature, there is a transcrescence of the tool which cannot be less than a certain minimum if the entire work surface is to be ground. Tools with transcrescence greater than said minimum will grind said surfaces, and the stroke need not be maximum. I have determined that transcrescences somewhat greater than the minimum required, permit relatively long strokes, and still permit adequate leewav for adjustment in stroke length so that the same tool can be used for grinding a range of surfaces of revolution varying from hypoeccentrie to hypereccentric, with the stroke length being shorter or longer as the surfaces are hypoeccentric or hypereccentric respectively. A range of bell shaped surfaces may similarly be ground by the same tool providing the transcrescence is sutiicient.

(6) The magnitude of the tool. Tools of larger overall diameter are used for the grinding of optical surfaces of large overall dimensions, and vice versa. The length of the stroke is generally proportional to the magnitude of the tool.

I have pointed out that the stroke length is a function, among other variables, of the diameter of the work surface. However, the actual work surface may be execssively large, so that the full extent of the work surface need not be ground since the excessive material will later be removed by reducing the diameter of the surface. Should it be desirable at any time to enlarge the area of the work surface being ground, the stroke length may be increased by adjustment of the apparatus.

If the stroke has been adjusted so that thc work surface is ground to its periphery, then the work piece should be circular in outline and the axis of revolution of the work piece and the work holder must coincide. I have made provision for proper centering and alignment of the work piece by designing and producing work holders which have a recessed circular area within which the work piece fits, so that it is centered and coaxial with the work holder. The work piece and work holder will then rotate smoothly about the common work-piece-work-holder axis of revolution during the grinding procedure. In PIG. 9 I have drawn a meridian section through a work holder and associated work piece which consists of a plastic contact lens button. The relatively large diameter of the work holder is useful in maintaining a relatively uniform rate of rotation of the work holder and work piece during the oscillation, when said rotation is produced as a result of the friction of the work surface against the surface of the rotating tool, rather than by a separate mechanism propelling the work holder and work piece. The work holder is made of metal, such as brass or iron, and as a result of its relatively large diameter, the angular momentum gained by said holder while it and the work piece traverse the tool, tends to keep said holder and work piece rotating at a substantially uniform rate during all phases of the oscillation. I have used a work holder like that depicted in FIG. 9 for the grinding of concave aspheric surfaces of revolution of contact lenses, supporting the work holder and work piece against the upper aspect of the tool by means of a pointed metal shaft, the point of which fits into a cone-shaped recess 30 on the back of the work holder with room to oscillate about the point. No motive force other than that resulting from thc fi ietion of the work surface against the rotating tool was required for producing the relatively uniform rate of rotation of the work piece and its holder, vwhich was maintained throughout the oscillation. The apparatus of this invention, as seen in FIGS. 25 to 32, however, also has provision of a separate motive power for rotation of the work holder and work piece when said rotation is not produced by the friction of the work piece in Contact with the rotating tool.

If, for a given work surface, the stroke is longer than necessary then at one end of the stroke the entire work surface will be clear of the tool, except for points of contact at the extreme edge of the work surface which touch the tool. The result is a blunting of the edge of the work surface, but the remainder of the work surface will not be deformed as long as it remains free of the tool. To avoid such blunting of the edge of the work surface, the stroke length is reduced to the point where grinding occurs just to the edge of the work surface.

For a tool of a given transcreseence and for a given aspheric work surface of a given diameter, the stroke length is adjusted so that the entire work surface is ground. If the same tool is used to grind another work surface of the same diameter but whose rate of change in curvature from the apex to the periphery is less than that of the rst work surface, the stroke can be reduced. With still another work surface with an even smaller rate of change of curvature, the stroke can be further reduced, and if finally a surface with no change in curvature is ground, the stroke is reduced to zero. Hence the same tool can be used to grind any number of different aspheric surfaces, and including spherical surfaces, by the appropriate adjustment of the stroke length. In the earlier example of the grinding of a contact lens concave aspheric surface of revolution wherein the equatorial radius of curvature of the tools was 7.5 mm., which was also the meridional radius of curvature of said tool at said equator, and the semi-meridian section of the tool had an elliptical profile of an ellipse of eccentricity 0.5, said tool was used to grind a concave prolate ellipsoid whose apical radius of curvature was 7.5 mm. and whose eccentricity was 0.7. The same tool can also be used to grind other prolate ellipsoids with the same apical radius of curvature, but with eccentricities of 0.6, 0.5, 0.4, 0, reducing the stroke length with decreasing eccentricity, until at zero eccentricity, there is no oscillation of the work piece.

Referring to FIG. 4, if the apex of the work surface is at point 3 along a meridian section of the tool, the surface generated will have a radius of curvature equal in length to 3-3'. Hence, the same tool may also be used to grind surfaces which not only diler in eccentricity or generalized ecceutricity, but which have different apical radii of curvature. For example, again referring to FIG. 4, a particular aspheric work surface might have a range of oscillation extending from point 2 to about point 4 along the meridian of the tool. The apical radius of curvature of the work surface would then be 2-2'.

Again referring to FIG. 4, if the work surface is first ground with its apex at point 4 along the meridian of the tool, the surface produced will have a radius of curvature equal to 4-4. The work piece may then be moved over the equator of the tool and oscillated for a range between said equator to about point 2 along the meridian, to grind a central aspheric area adjoining the peripheral spherical z'one, with the apical radius of curvature being that of the equator of the tool; or the work piece may be made to oscillate between point 1 and point 2, to grind a central aspheric area whose apical radius of curvature is 1-1', said central aspheric area adjoining the peripheral spherical zone; or the work piece may be placed over the so equator, or at any desired point between the equator and point 4, and not oscillated, thereby to grind a central spherical area of one radius adjoining the peripheral spherical zone of another radius.

Again referring to FIG. 4, the work piece may be placed at a particular point along a meridian, the equator for example, and not oscillated, thereby to grind a spherical surface, and then the work piece can be oscillated in a range from about point 2 along the meridian to about point 4, thereby to grind a peripheral aspheric zone adjoining the central spherical zone.

Again referring to FIG. 4, the work piece may at first be oscillated between the equator and about point 2 along the meridian of the tool, thereby to grind an aspheric surface, with the apical radius of curvature being that of the equator of the tool, and then oscillated between a range from about point 3 to about point 4, thereby to grind a peripheral aspheric zone adjoining the central aspheric area.

The above examples demonstrate the great versatility of this embodiment of this invention for the grinding of concave aspheric surfaces of revolution on optical material, a single tool being capable of grinding many different surfaces to a high standard of perfection.

As was pointed out early in the description of this invention, the essential features of the tool of this embodiment of this invention is its transcrescence, which is a continuously and regularly increasing transmeridional radius of curvature in the direction of decreasing diameter of circles of latitude of the tool, the transrneridional radius of curvature being longer than the meridional radius of curvature, for a zone of the tool lying between the equator of the tool and a distal circle of latitude, or for a zone of the tool surface lying between a circle of latitude of the tool proximal to the equator and a circle of latitude distal to the equator of the tool. The tool used in the above examples of grinding according to this invention is, therefore. not the only form which may be used in the application of this invention, as will now be described.

As clearly shown in FIG. 4, to achieve the essential feature of transcrescence in a zone of a tool, it is necessary that the locus of centers of curvature of the portion BA of a semi-meridian section limited by said zone, that is, the evolute portion CV for said semi-meridian section portion, lie on the same side of the axis of revolution of said tool X'X as the semi-meridian section being considered. Several examples of tool forms differing from each other but all having the essential feature of transcrescence, will now be given.

FIG. 10 is a view perpendicular to a plane section of a tool, resembling FIG. 4, the difference being that the equatorial circle of the tool represented by FIG. 4 is not umbilical, since the axis of revolution X'X of the tool is intersected perpendicularly by minor axis BB' of the elliptical semi-meridian section at a distance from point B on said elliptical arc which is less than the meridional radius of curvature at point B. Axis X'X of the tool intersects the evolute of said elliptical arc at point 1', so that the circle of latitude through point 1 is umbilical, the radius of curvature at point 1 being 1-1'. The tool surface from said umbilical circle of latitude through increasingly distal circles of latitude, of decreasing diameter, has the essential quality of transcrescence, since the locus of centers of curvature for the portion 1-A of the semi-meridian section corresponding to said tool zone between the umbilical circle of latitude through point 1 and the circle of latitude of the tool farthest from the equator, i.e., the most distal circle of latitude at point A, lie on the same side of axis X'X. However the zone of the tool surface between the equator and said umbilical circle of latitude does not have transcrescence, and accordingly said zone is not used for grinding according to this embodiment of this invention. The range of oscillation of the work surface is therefore such that its apex does not extend into the zone of said tool between its equator and said umbilical circle of latitude.

FIG. 11 is a view perpendicular to a plane section of a tool resembling FIG. 4, the difference being that the equatorial circle is not umbilical, since axis of revolution X'X of the tool is intersected perpendicularly by minor axis BB of the elliptical arc at a distance from point B on said arc which is greater than the meridional radius of curvature at point B. Axis X'X therefore does not intersect the evolute of the elliptical semi-meridian section at any point, so that the tool has no umbilical line, but does have the essential feature of transcrescence at all points, since the evolute, which is the locus of the centers of curvature of said semi-meridian section, lies on the same side of axis X'X as the semi-meridian section. Consequently the range of oscillation of the work surface can extend from the equator of the tool through all increasingly distal circles of latitude of the tool.

FIGS. l2, 13 and 14 are quite similar to FIGS. 4, 10 and 11, except that arc ABA is that of a cycloid. By inspection of FIGS. 12, 13 and 14, it can be seen that the tool axis X'X has the same relative positions with respect to the evolute of the cycloid CA and CA' as it does to the evolute of the elliptical arc of FIGS. 4, 10 and l1 respectively. Consequently the range of oscillation of the work surface for the three tools whose principal sections are shown in FIGS. l2, 13 and 14 resemble the range of oscillations for the work surface with the tools whose principal sections are shown in FIGS. 4, 10 and l1.

FIGS. 15, 16 and 17 are quite similar to FIGS. 4, 10 and 11 except that arc A'BA is that of an involute of a circle. By inspection of FIGS. 15, 16 and 17, it can be seen that the tool axis X'X has the same relative positions with respect to the circular evolute CF and CF of said involute as it does to the evolute of elliptical arcs of FIGS. 4, 10 and 11 respectively. Consequently, the range of oscillations of the work surface for the three tools whose principal sections are shown in FIGS. 15, 16 and 17 respectively is similar to the range of oscillations of the work surface for the three tools whose principal sections are shown in FIGS. 4, 10 and 1l respectively.

FIGS. 18, 19 and 20 are similar to FIGS. 15, 16 and 17 except that the degree of transcrescence has been modified by a variation in the size of the circular evolute CF and CF'.

FIG. 21 represents the limiting case of FIGS. 18, 19 and 20, in which the circular evolute has been reduced to a point 0, said point lying on the same side of axis XX as does the circular semi-meridian arc. It is apparent by inspection of FIG. 2l that the essential feature of transcrescence is present at all points from the equator to the rnost distal circle of latitude.

FIG. 22 is a view perpendicular to a plane section of a tool whose semi-meridian section is an elliptical arc, with the axis of revolution XX being perpendicular to the major axis of the elliptical arc at its mid-point, the geometrical center of the tool. By inspection, it can be seen that the essential feature of transcrescence is present in the tool whose meridian section is depicted in FIG. 22, even though the meridional radius of curvature increases continuously and regularly along with the transmeridional radius of curvature.

FIG. 23 is a view perpendicular to a meridian section of a tool similar to that whose meridian section is depicted in FIG. 22, except that axis XX intersects the major axis of the elliptical semi-meridian section at a distance greater than OA. Consequently the essential feature of transcrescence is present at all points along the tool from the equator to the most distal circle of latitude.

FIG. 24 is a view perpendicular to a meridian section of a tool similar to that whose meridian section is depicted in FIG. 22, except that axis XX intersects the major axis of the elliptical semi-meridian section at a distance less than OA. Consequently the essential feature of transcrescence is limited to a zone of the tool surface between the equator of said tool and a circle of latitude through a point (point 4 of FIG. 24) where the normal through said point extends from the intersection of the evolute and axis XX (point 4' of FIG. 24).

It is apparent from the above description of tools in this first embodiment that many variations in design are possible, while retaining the essential feature of transcrescence. In general, I prefer to use tools constructed like those depicted in FIGS. 4, and 11 because of their simplicity in design and construction, and I also prefer to use tools constructed like those of FIG. 21, again because of their simplicity in design and construction. It is to be understood that the above variations in tool design, and others not described, are to be considered within the domain of this invention when the essential feature of transcrescence is present.

FIG. 25 is a front elevational view and FIG. 26 is a side elevational view of the apparatus of this invention. The base 10 of the apparatus consists of a heavy metal table whose upper surface is substantially horizontal. Portions of the top and front side have been cut away to permit the fitting and adjustability of other parts of the apparatus. Attached to the front side of the base by means of screws a and 20b which permit vertical adjustment is vertically adjustable plate 23, through an upper extension 23a of which horizontal pivot 24 passes horizontally to serve also as the pivot for rectangular arm which can be adjusted in inclination about pivot 24. Attached for rotation to the inner face of arm 25 is a precision spindle or shaft 26 which is substantially parallel to the edges of rectangular arm 25, and which is caused to rotate about its longitudinal axis by means of electric motor 27 which is also attached to arm 25. Adjustment of the slope of arm 25 therefore brings about the same slope in spindle shaft 26. Attached to arm 25 by means of screws 31a, 31b and 32a, 32b are circular arms 33 and 34 containing circular slots 33a and 34a centered about the axis of pivot 24. To adjust the inclination of spindle shaft 26, lock screws 35 and 36 within said circular slots and threaded into the front face of base 10 are loosened, arm 25 is adjusted to the desired position, and lock screws 35 and 36 are then tightened.

Attached to spindle shaft 26 by means of screw threads is tool 37 coaxial with shaft 26. Placed against the upper aspect of tool 37 and held to it by the force of gravity is work piece 38, suitably held in `a recess in the work holder 39, which in turn is maintained in position by the cone-shaped tip of steel shaft or pin 40, said tip fitting, with loom for oscillation, in a cone-shaped recess 41 on the upper side of work holder 39, shown in cross sectional view in FIG. 9. The apex of recess 4l is on the axis of revolution of the work piece 38. Shaft 40 is slidably held by horizontal shaft support 42. Attached by means of a set screw to the ripper end of shaft 40 is adjustable weight 43 which can be increased or decreased as desired to increase or decrease the pressure between the work surface and the tool. Horizontal shaft support 42 is attached by face plate 44 and set screw 45 to rocker arm 46 which in turn is rigidly attached and locked by means of set screw 47 to horizontal pivot shaft 48 whose axis of revolution is perpendicular to the vertical plane containing the axis of revolution of spindle shaft 26 and substantially coaxial with pivot 24. Shaft 48 is rotatably mounted in block 49 which is xed to base 10. Attached to the opposite end of horizontal pivot shaft 48 is rocker arm 50. the shaft 48 extending into arm 50 and being rigidly locked in position by means of set screw 5l. Extending rigidly from rocker arm 50 is a horizontal rod 52 of circular cross section, the axis of said rod being parallel to the axis of pivot 48. Rod 52 is held rmly against vertical rod 53, of circular cross section, by means of springs 54 extending from the upper end of rocker arm 50 to vertical rod support 55 attached to base 10. Vertical rod 53 is attached to a horizontal slide member 56, which is adjustable along horizontal slideways 57, where it can be locked in position by means of a set screw S8. Horizontal sldeway 57 is rmly attached to vertical shaft 59 which is attached to rotatable vertical shaft 6l) `by means of set screws 60a, said shaft extending vertically from reduction gearing 61 driven by motor 62 which causes shaft S9 to rotate about 60 revolutions per minute.

It can be seen that the extent of angular movement of rocker arms 46 and 50 is adjustable by controlling the separation of the axes of vertical rod 53 and vertical shaft S9, with a consequent control of the stroke of the work surface along the tool.

Not shown is a. rheostat which controls the rate of revolution of motor 27 so that the tool 37 rotates about revolutions per minute. However, slower or faster rates of revolution of this tool may be used. The duration of the grinding procedure is controlled by clock control 63, which can be set to permit grinding for selected periods of time.

In order to achieve relatively uniform pressure between the work surface and the tool throughout the stroke, the slope of arm 25 is adjusted so that for the required arcuate path of the work surface along the tool, the axis of revolution of the work surface and the work holder will incline about equally with respect to the vertical at each end of the stroke. If it is desired to have greater pressure between the work surface and the tool toward one end of the stroke, arm 25 can be adjusted so that the axis of revolution of the work surface and work holder will be approximately vertical at the desired end of the stroke. Rocker arm 46 must at the same time be adjusted so the stroke appropriate for the work surface and tool is utilized.

The axes of pivots 24 and 48 are parallel and coaxial or closely approaching that condition. When not coaxial the separation of said axes is brought about by adjustment of plate 23, said adjustment being used to raise or lower the tool 37 so that the axis of pivot 48 will pass through the tool in the vicinty of its geometrical center. This adjustment is performed to minimize the difference in slopes which develop during a stroke, be-

15 tween the common axis of revolution of the work surface and work holder, and the axis of shaft 40, thereby assuring the least friction between the point tip of shaft 40 and the conical recess 41 in the steel bearing surface on the back of work holder 39 into which the tip of shaft 40 fits.

Shaft 40, substantially coaxial with the axis of rotation of work piece 38, oscillates in a plane containing the axis of rotation of tool 37, or in a plane closely approximating such plane. The axis of work piece 38 is always at an angle to the axis of tool head 37.

Generally, rocker arms 46 and 50 are parallel, but as described above, they may be adjusted skew to each other about the axis of pivot 48.

The appartus may be modified in different ways without departing from the basic design. One such modification would be the use of cams to control the oscillation of the work surface rather than rod 53` and the slideway 57. Said cams would extend directly from shaft 59 to contact rod S2. The use of cams rather than rod 52 and slideway 57 makes possible a large variety of oscillatory movements other than substantially simple harmonic motion, enlarging the scope of the apparatus in its applications.

With the apparatus described, the work piece is rotated about its axis of revolution (normal to the apex of the generated or ground surface) by friction contact with the rotating tool 37.

The apparatus may also be modified by utilizing a power supply for rotation of the work piece during all phases of the oscillation of the work piece, rather than depending upon friction between the work surface and tool to cause rotation of the work piece and work holder. This merely requires a motor on arm 42 driving a pulley in the position of weight 43.

Heretofore, the specification has described the first embodiment of this invention, wherein the tool is the generally convex surface of revolution and the work surface is the generally concave surface of revolution. By a reversal of parts so that the generally convex surface of revolution becomes the work surface while the generally concave surface of revolution is the tool, the second embodiment of this invention is achieved.

iIn this second embodiment, work surfaces having principal sections like those represented in FIGS. 3, 4, 7, `8, and l through 24, can be generated, ground and polished in the zone of those surfaces having the essential feature of transcrescence, by tools of generally concave shape of the forms depicted in FIGS. l and 2, said tools being characterized by being surfaces of revolution having eccentricity or generalized eccentricity, as previously described, wherein the meridional curvature decreases from the apex to the periphery of the surface. The conicoids of revolution are examples of said tools and are satisfactory for the production of said surfaces.

The apparatus and motions for the production of these generally toric convex surfaces of revolution differs only slightly from that utilized for the generally concave surfaces of revolution described in connection with the first embodiment of this invention. In the second embodiment, the generally concave tool is most often made to oscillate equidistantly across the equator of the work surface for a relatively wide zone which includes the equator when it is either umbilical or has transcrescence. When the work piece is to be ground substantially equidistantly on opposite sides of the equator, for this embodiment of the invention, the equatorial plane is made vertical by adjusting shaft 26 to a horizontal position. This insures substantially uniform pressure of the tool upon the work piece on both sides `of the equator. Most often the equator of said work surface is one of the principal meridians of said surface when it is used as a finished optical surface of a lens or lens system.

When a zone of the work surface which is to include the equator is desired, I prefer to use two of the generally concave polishing tools of this second embodiment oscillating in opposite directions and being positively rotated in opposite directions by motor drive so as to equalize the generating or grinding or polishing effects on both sides of the equator. If, however, the desired finished surface is to include a zone on one side of the equator of the work piece only, only one tool may be all that is required and it may be caused to rotate about its axis of revolution by the frictional effects of the work surface only, or, of course, it may be driven also. In this case, the axis of revolution of the work piece is inclined so as to provide relatively uniform pressure between the work piece and tool in said zone.

The apparatus for carrying out this second embodiment of the invention is identical with that described in connection with FIGS. 25, 26 and 27 except for the difierences now to be described. FIG. 29 shows the changes necessary to be made in the apparatus shown in FIGS. 25, 26 and 27. The block 49 is like that shown in FIG. 26 as is also the pivot shaft 48. The equipment attached to the shaft 48 by set screw 47 is different. In place of arm 46, there is secured to shaft 48 arm 46' which has a squared upper end passing through a squared opening 71 in arm 42'. A helical spring 72 secured between arm 42 and collar 73, fastened at the upper end of arm projection 70, counterbalances part of the weight of arm 42 and its load. Mounted on arm 42' is a small electric motor 74 whose drive shaft 7S operates a pulley 76 connected by drive belt 77 with a pulley 78 fixed to the upper end of shaft 79 which passes downwardly throught thrust bearings 80 in arm 42 and becomes rigidly part of rod 40' which is analogous to rod 40 in FIG. 26. Convex work piece 37 is now rotated by shaft 26' in the position of parts 37 and 26 of the first ernbodiment. The concave tool member 38' now takes the place of form work piece 38 on the lower end of the rod. 38 is guided at the lower end of rod 40' by having the pointed lower end of rod 40 enter into a conical opening 41' in the tool 38 and centrally thereof. A yoke 81 is fixed to the lower end of rod 40 and has bifurcated arms which extend downwardly and loosely into recesses 82 in the tool 38. This provides positive rotation of tool 38' by means of motor 74 and the connections shown while at the same time permitting accommodation of the tool 38 to the work piece 37' as the tool is oscillated by shaft 48 and arms 46 and 42'. It should be understood that in this embodiment, as in the rst embodiment, the machine is assembled to operate on the work piece with the member 38, in the first embodiment, or 38', in the second embodiment, firmly against the rod 40 or 40'. After that, gravity maintains contact between members 38 and 37 in the first embodiment or 38 and 37 in the second embodiment.

In place of the work piece 37 just described in the second embodiment, there may be substituted a plurality of work pieces as illustrated in FIG. 3l. To shaft 26' there is secured a wheel 82 on the peripheral work surface of which there are aflixed, as by adhesive or mechanically, a plurality of work pieces 83. Each of these pieces might be a blank for the formation of a generally toric lens commonly in use. When these work pieces 83 are rotated by shaft 26 in the apparatus of FIG. 29, a plurality of generally convex work pieces `may be formed utilizing a suitable generally concave tool 38'.

For polishing lenses made according to the first ernbodiment of this invention, the tool head 37 is preferably covered over a major portion thereof by a piece of soft cloth 84 as shown in FIG. 28. This is held in position by adhesive. The soft cloth is impregnated with the polishing medium. In like manner, in the second embodiment, it is preferable for polishing to adhere a soft piece of cloth, such as Velveteen, to the concave face of tool 38' and impregnate the cloth with the polishing medium In FIG. 32 is shown a substitute for the oscillation control described in connection with FIGS. 25 and 26 which is produced by the parts 52, 53, 56, 57 and S9. In

FIG. 32, to the upper end of shaft 59 is rigidly secured a cam 85 having a vertical face contacting rod 52 rigidly attached to arm Sl) in the position of rod 52 of the first embodiment. Here again, spring 54 maintains Contact between rod 52' and the cam 85. lt is obvious that by using this cam construction, various motions, other than harmonic, if desired, may be provided for the relative oscillation between the work piece and the tool of this invention.

Wherever in the specification and claims I have used the term grinding I mean to include also generating and polishing.

What is claimed is:

1. Apparatus for generating, grinding or polishing aspheric surfaces of revolution on optically useful material utilizing abrading action between opposing nonmatching aspheric surfaces of a work piece and a tool piece, one of said pieces comprising a generally toric convex aspheric surface of revolution having transcrescence and the other of saizl pieces comprising a generally concave aspheric surface of revolution of generally conicoid type; comprising a base, a first shaft rotat ably mounted on said base and carrying said generally convex piece for rotation thereby about the common axis of said first shaft and said convex piece, said convex piece being a surface of revolution having transcrescence wherein at all points along all meridian sections containing the common axis of revolution of said piece and of said rst shaft, the transmeridional radius of curvature increases continuously and regularly from a circle of latitude at the equator, or from a proximal circle of latitude near the equator, of said piece outwardly to a maximum value at a distal circle of latitude farthest from the equator of said piece. means for rotating said first shaft and convex piece, a second shaft supported on said base approximately coplanar with said first shaft, the

axis of said second shaft at an angle to the axis `of said rst shaft, means mounting said generally concave piece rotatable substantially about the axis of said second shaft in position to engage said generally convex piece, means for rotating said generally concave piece, means for causing relative pressure between said non-matching pieces, and means mounted on said base for causing relative oscillation between said pieces along a meridian of said generally toric convex surface of revolution having said transcrescence, said engagement traversing the zone of transcrescence of said convex piece.

2. The method of generating, grinding or polishing aspheric surfaces of revolution by abrasive engagement between a Work piece surface and a non-matching tool piece surface, one of said surfaces being a positive aspheric surface of revolution of generally toric shape having the property of transcrescence, the other of said surfaces being a generally negative aspheric surface 0f revolution of generally conicoid shape, including supporting said piece with the positive surface of revolution for rotation about its axis of revolution, said positive aspheric surface having transcrescence wherein the transmeridional radius of curvature at all points along all meridian sections Of said positive piece increases continuously and regularly from a circle of latitude at the equator, or from a proximal circle of latitude near the equator, of said positive piece outwardly to a maximum value at a distal circle of latitude farthest from said equator of said positive piece surface, placing in contact with said positive surface said negative surface and maintaining said two surfaces in abrading contact with cach other, rotating each of said surfaces about its respective piece axis while causing relative oscillation between said two surfaces in a generally meridional direction of said positive surface with said abi-ailing contact traversing the zone of transcrescence of said positive surface and causing said contact between said two surfaces to valy in a continuously changing pattern of Contact involving as a single area the apex of said negative surface and a corresponding approximately equatorial area of said positive surface and progressing from said single area to a symmetrical pair of areas of Contact involving the periphery of said concave surface and a corresponding symmetrical pair of areas laditudinally of said approximately equatorial area on said positive surface and back again in a cyclic pattern as a consequence of said oscillation and said property of transcrescence of said positive piece, while maintaining the axes of revolution of said surfaces of said two pieces at all times intersecting.

3. Apparatus as defined in claim 1 including means for varying the inclination of the axis of said first shaft.

4. Apparatus as defined in claim 1 including `means for varying the extent of said oscillation along said meridian.

5. Apparatus as defined in claim 1 wherein said means tounting said generally concave piece rotatably on said second shaft is a low friction bearing `whereby said generally concave piece may be caused to rotate solely by engagement with said rotating generally convex piece.

6. Apparatus as defined in claim I, including means for positively rotating said generally concave piece.

7. The method of claim 2, wherein said work piece surface is the negative aspheric surface of revolution of generally conicoid shape, said abrading tool surface is the positive aspheric surface of revolution of generally torio shape having the property of transcrescence, and said work piece surface is oscillated wholly on one side or the equator of said tool surface.

8. The method of claim 2, wherein said work piece surface is the positive aspheric surface of revolution of generally torie shape having the property of transcrescence, said abrading tool surface is the negative aspehcric surface of revolution of generally conicoid shape, and said tool surface is oscillated across and on both sides of the equator of said work piece surface.

References Cited UNITED STATES PATENTS 1,659,277 2/ 1928 Maynard. 1,527,045 2/1925 Howland. 1,331,037 2/192() Sullivan. 2,087,687 7/1937 Houchin. 2,247,706 7/1941 Goddu.

JAMES L. JONES, JR., Primary Examiner U.S. Cl. X.R. 51-284 

